Is F/A the stress at every point?

No. F/A is an average. Uniform axial normal stress requires a centric resultant and a section sufficiently away from load introduction or discontinuities. Direct-shear stress distribution generally is not uniform.

When does M/W give bending stress?

It gives nominal extreme-fiber normal stress for the documented elastic section modulus about the correct bending axis within the linearly elastic simple-flexure model.

Does this worksheet prove safety?

No. It performs no material selection, stress concentration, combined-stress, stability, fatigue, fracture, code or acceptance assessment.

Controlled nominal-mechanics worksheet

Average axial, average direct-shear and elastic bending stress

Evaluate one documented section and one internal resultant. The worksheet reports an average axial/direct-shear value or a nominal extreme-fiber elastic bending value—never a local peak or design acceptance.

Signed resultantsExact unit normalizationNo presetsNo allowable stress

Boundary: determine internal resultants from a valid free-body analysis first. Holes, threads, multiple shear planes, eccentricity, contact, stress concentration, beam shear distribution, multiaxial loading, buckling, plasticity, fatigue and fracture are outside this scalar worksheet.

1. Calculation mode and section inputs

Režim *

Internal resultant force *

Use the internal axial resultant N or direct-shear resultant V at the documented cut—not an unverified external load.

Force unit *

Resisting area A *

Document net/gross area, holes/threads and number of shear planes in the section record.

Area unit *

Internal bending moment M *

Moment unit *

Elastic section modulus W = I/c *

Use the modulus for the stated bending axis and reported extreme fiber; asymmetric sections may require separate W values.

Section-modulus unit *

2. Controlled section record

Record / item ID *

Cut, member and location *

Drawing / model / calculation source *

Edition / revision / date *

Internal-resultant derivation and load case *

Area or W axis/face basis *

Material regime and model conditions *

Analyst / checker *

Record date *

Poznámky

3. Confirmations

I derived the entered internal resultant at the stated cut from a controlled load case and sign convention.I verified the resisting area or elastic section modulus, including axis/face, net/gross basis, holes/threads and shear-plane count where applicable.I verified the selected mode’s assumptions: centric/far-field axial average, direct-shear average only, or linearly elastic simple bending with the correct W.I will not use this nominal scalar result as a local peak, combined stress, allowable value, safety factor or code/design acceptance.

4. Result

Signed nominal value-

Magnitude-

Klasifikace-

Method and applicability

Average axial normal stress

σ_průměr = N/A

Internal axial resultant through the section centroid.
Uniform average sufficiently away from load introduction and discontinuities.
Not eccentric bending or a local notch/thread stress.

Average direct-shear stress

τ_průměr = V/A

Reports only the sectional average.
The real distribution generally is not uniform.
Not the beam formula VQ/(It), bearing stress or torsional shear.

Nominal elastic bending stress

σ_nom = M/W = Mc/I

Linearly elastic simple flexure and correct neutral axis.
W = I/c for the stated axis and extreme fiber.
Not plastic, composite, curved-beam or local peak stress.

Dimensional identities used: N/mm² = MPa; N·mm/mm³ = MPa. The sign is preserved from the documented internal-force convention. Strength, allowables, partial/safety factors and acceptance criteria are deliberately absent.

Sources and classification

University of Illinois Mechanics Reference — Stress: distinguishes point stress from sectional averages; states the centric/far-field conditions for uniform axial average and that direct-shear distribution cannot generally be assumed uniform.
University of Illinois Mechanics Reference — Bending: linearly elastic flexural relation σ = −My/I, maximum magnitude |M|/S and S = I/c.
NIST SP 811 Appendix B: exact inch/pound-force basis and published stress conversion factors.

Klasifikace: these are bounded general-mechanics relationships, not formulas attributed to ISO, ASME, ASTM, EN or another design standard. Any actual allowable, resistance, load combination, stress concentration, fatigue method or acceptance rule requires its controlled governing source.